Optimisation approaches for the synthesis of water treatment plants

•Optimal flowsheet design of water treatment is proposed by an overall system approach.•Two non-linear and one linear fractional models are formulated to minimise the water production cost to meet final product requirements.•Application to two illustrative examples, i.e. seawater desalination and surface water treatment.•Linear fractional model demonstrates superior performance with respect to solution quality and CPU times.

Efficient water treatment design has progressively been growing in importance as the usage of water resources increases with population rise and industrial development. Their availability has been reduced with the more evident effects of climate change. Addressing this challenge necessitates more and efficient purification plants which can be realised by optimal design at conceptual stage. In this work, a mixed integer nonlinear programming (MINLP) model for the synthesis and optimisation of water treatment processes is proposed. Due to its numerous non-linearities and consequently, its non-stability, various linearisation, approximation and reformulation techniques have been implemented. Consequently, two improved formulations are derived, i.e. a partially linearised MINLP (plMINLP) and a mixed integer linear fractional programming (MILFP) models. The applicability of the mathematical formulations are investigated in case studies of seawater desalination and surface water treatment for the production of potable water. Finally, the models performance is analysed and compared against each other.